LMFDB - Embedded newform 8002.2.a.e.1.67

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.67
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.54982 q^{3} +1.00000 q^{4} -0.793092 q^{5} -2.54982 q^{6} +3.15095 q^{7} -1.00000 q^{8} +3.50157 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.54982 q^{3} +1.00000 q^{4} -0.793092 q^{5} -2.54982 q^{6} +3.15095 q^{7} -1.00000 q^{8} +3.50157 q^{9} +0.793092 q^{10} +4.06606 q^{11} +2.54982 q^{12} -1.86768 q^{13} -3.15095 q^{14} -2.02224 q^{15} +1.00000 q^{16} -5.00588 q^{17} -3.50157 q^{18} -2.29165 q^{19} -0.793092 q^{20} +8.03434 q^{21} -4.06606 q^{22} +2.06029 q^{23} -2.54982 q^{24} -4.37100 q^{25} +1.86768 q^{26} +1.27891 q^{27} +3.15095 q^{28} +2.29563 q^{29} +2.02224 q^{30} +3.84994 q^{31} -1.00000 q^{32} +10.3677 q^{33} +5.00588 q^{34} -2.49899 q^{35} +3.50157 q^{36} +4.83293 q^{37} +2.29165 q^{38} -4.76224 q^{39} +0.793092 q^{40} +7.98927 q^{41} -8.03434 q^{42} +3.37893 q^{43} +4.06606 q^{44} -2.77707 q^{45} -2.06029 q^{46} -4.16864 q^{47} +2.54982 q^{48} +2.92847 q^{49} +4.37100 q^{50} -12.7641 q^{51} -1.86768 q^{52} -0.864013 q^{53} -1.27891 q^{54} -3.22476 q^{55} -3.15095 q^{56} -5.84330 q^{57} -2.29563 q^{58} +11.8178 q^{59} -2.02224 q^{60} +2.40674 q^{61} -3.84994 q^{62} +11.0333 q^{63} +1.00000 q^{64} +1.48124 q^{65} -10.3677 q^{66} +7.94303 q^{67} -5.00588 q^{68} +5.25337 q^{69} +2.49899 q^{70} -5.71069 q^{71} -3.50157 q^{72} -10.3122 q^{73} -4.83293 q^{74} -11.1453 q^{75} -2.29165 q^{76} +12.8119 q^{77} +4.76224 q^{78} +8.43614 q^{79} -0.793092 q^{80} -7.24372 q^{81} -7.98927 q^{82} +11.1952 q^{83} +8.03434 q^{84} +3.97012 q^{85} -3.37893 q^{86} +5.85343 q^{87} -4.06606 q^{88} +10.6447 q^{89} +2.77707 q^{90} -5.88496 q^{91} +2.06029 q^{92} +9.81664 q^{93} +4.16864 q^{94} +1.81749 q^{95} -2.54982 q^{96} +2.85403 q^{97} -2.92847 q^{98} +14.2376 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.54982	1.47214	0.736069	−	0.676907i	$-0.236680\pi$
$3$	2.54982	1.47214	0.736069	+	0.676907i	$0.236680\pi$
$4$	1.00000	0.500000
$5$	−0.793092	−0.354682	−0.177341	−	0.984150i	$-0.556749\pi$
$5$	−0.793092	−0.354682	−0.177341	+	0.984150i	$0.556749\pi$
$6$	−2.54982	−1.04096
$7$	3.15095	1.19095	0.595473	−	0.803375i	$-0.296965\pi$
$7$	3.15095	1.19095	0.595473	+	0.803375i	$0.296965\pi$
$8$	−1.00000	−0.353553
$9$	3.50157	1.16719
$10$	0.793092	0.250798
$11$	4.06606	1.22596	0.612982	−	0.790097i	$-0.289970\pi$
$11$	4.06606	1.22596	0.612982	+	0.790097i	$0.289970\pi$
$12$	2.54982	0.736069
$13$	−1.86768	−0.518001	−0.259001	−	0.965877i	$-0.583393\pi$
$13$	−1.86768	−0.518001	−0.259001	+	0.965877i	$0.583393\pi$
$14$	−3.15095	−0.842126
$15$	−2.02224	−0.522140
$16$	1.00000	0.250000
$17$	−5.00588	−1.21410	−0.607052	−	0.794662i	$-0.707648\pi$
$17$	−5.00588	−1.21410	−0.607052	+	0.794662i	$0.707648\pi$
$18$	−3.50157	−0.825328
$19$	−2.29165	−0.525741	−0.262871	−	0.964831i	$-0.584669\pi$
$19$	−2.29165	−0.525741	−0.262871	+	0.964831i	$0.584669\pi$
$20$	−0.793092	−0.177341
$21$	8.03434	1.75324
$22$	−4.06606	−0.866887
$23$	2.06029	0.429600	0.214800	−	0.976658i	$-0.431090\pi$
$23$	2.06029	0.429600	0.214800	+	0.976658i	$0.431090\pi$
$24$	−2.54982	−0.520479
$25$	−4.37100	−0.874201
$26$	1.86768	0.366282
$27$	1.27891	0.246126
$28$	3.15095	0.595473
$29$	2.29563	0.426287	0.213144	−	0.977021i	$-0.431630\pi$
$29$	2.29563	0.426287	0.213144	+	0.977021i	$0.431630\pi$
$30$	2.02224	0.369209
$31$	3.84994	0.691469	0.345735	−	0.938332i	$-0.387630\pi$
$31$	3.84994	0.691469	0.345735	+	0.938332i	$0.387630\pi$
$32$	−1.00000	−0.176777
$33$	10.3677	1.80479
$34$	5.00588	0.858501
$35$	−2.49899	−0.422407
$36$	3.50157	0.583595
$37$	4.83293	0.794529	0.397264	−	0.917704i	$-0.369960\pi$
$37$	4.83293	0.794529	0.397264	+	0.917704i	$0.369960\pi$
$38$	2.29165	0.371755
$39$	−4.76224	−0.762569
$40$	0.793092	0.125399
$41$	7.98927	1.24771	0.623857	−	0.781538i	$-0.285565\pi$
$41$	7.98927	1.24771	0.623857	+	0.781538i	$0.285565\pi$
$42$	−8.03434	−1.23973
$43$	3.37893	0.515283	0.257641	−	0.966241i	$-0.417055\pi$
$43$	3.37893	0.515283	0.257641	+	0.966241i	$0.417055\pi$
$44$	4.06606	0.612982
$45$	−2.77707	−0.413981
$46$	−2.06029	−0.303773
$47$	−4.16864	−0.608059	−0.304029	−	0.952663i	$-0.598332\pi$
$47$	−4.16864	−0.608059	−0.304029	+	0.952663i	$0.598332\pi$
$48$	2.54982	0.368034
$49$	2.92847	0.418352
$50$	4.37100	0.618153
$51$	−12.7641	−1.78733
$52$	−1.86768	−0.259001
$53$	−0.864013	−0.118681	−0.0593407	−	0.998238i	$-0.518900\pi$
$53$	−0.864013	−0.118681	−0.0593407	+	0.998238i	$0.518900\pi$
$54$	−1.27891	−0.174037
$55$	−3.22476	−0.434827
$56$	−3.15095	−0.421063
$57$	−5.84330	−0.773964
$58$	−2.29563	−0.301431
$59$	11.8178	1.53855	0.769275	−	0.638918i	$-0.220618\pi$
$59$	11.8178	1.53855	0.769275	+	0.638918i	$0.220618\pi$
$60$	−2.02224	−0.261070
$61$	2.40674	0.308151	0.154076	−	0.988059i	$-0.450760\pi$
$61$	2.40674	0.308151	0.154076	+	0.988059i	$0.450760\pi$
$62$	−3.84994	−0.488943
$63$	11.0333	1.39006
$64$	1.00000	0.125000
$65$	1.48124	0.183725
$66$	−10.3677	−1.27618
$67$	7.94303	0.970396	0.485198	−	0.874404i	$-0.338748\pi$
$67$	7.94303	0.970396	0.485198	+	0.874404i	$0.338748\pi$
$68$	−5.00588	−0.607052
$69$	5.25337	0.632431
$70$	2.49899	0.298687
$71$	−5.71069	−0.677734	−0.338867	−	0.940834i	$-0.610044\pi$
$71$	−5.71069	−0.677734	−0.338867	+	0.940834i	$0.610044\pi$
$72$	−3.50157	−0.412664
$73$	−10.3122	−1.20696	−0.603478	−	0.797380i	$-0.706219\pi$
$73$	−10.3122	−1.20696	−0.603478	+	0.797380i	$0.706219\pi$
$74$	−4.83293	−0.561817
$75$	−11.1453	−1.28694
$76$	−2.29165	−0.262871
$77$	12.8119	1.46006
$78$	4.76224	0.539218
$79$	8.43614	0.949139	0.474570	−	0.880218i	$-0.342604\pi$
$79$	8.43614	0.949139	0.474570	+	0.880218i	$0.342604\pi$
$80$	−0.793092	−0.0886704
$81$	−7.24372	−0.804858
$82$	−7.98927	−0.882267
$83$	11.1952	1.22884	0.614418	−	0.788981i	$-0.289391\pi$
$83$	11.1952	1.22884	0.614418	+	0.788981i	$0.289391\pi$
$84$	8.03434	0.876618
$85$	3.97012	0.430620
$86$	−3.37893	−0.364360
$87$	5.85343	0.627554
$88$	−4.06606	−0.433443
$89$	10.6447	1.12833	0.564166	−	0.825662i	$-0.309198\pi$
$89$	10.6447	1.12833	0.564166	+	0.825662i	$0.309198\pi$
$90$	2.77707	0.292729
$91$	−5.88496	−0.616911
$92$	2.06029	0.214800
$93$	9.81664	1.01794
$94$	4.16864	0.429962
$95$	1.81749	0.186471
$96$	−2.54982	−0.260240
$97$	2.85403	0.289783	0.144892	−	0.989448i	$-0.453717\pi$
$97$	2.85403	0.289783	0.144892	+	0.989448i	$0.453717\pi$
$98$	−2.92847	−0.295820
$99$	14.2376	1.43093
$100$	−4.37100	−0.437100
$101$	−3.94531	−0.392573	−0.196286	−	0.980547i	$-0.562888\pi$
$101$	−3.94531	−0.392573	−0.196286	+	0.980547i	$0.562888\pi$
$102$	12.7641	1.26383
$103$	10.4081	1.02554	0.512772	−	0.858525i	$-0.328619\pi$
$103$	10.4081	1.02554	0.512772	+	0.858525i	$0.328619\pi$
$104$	1.86768	0.183141
$105$	−6.37197	−0.621841
$106$	0.864013	0.0839204
$107$	15.6475	1.51270	0.756352	−	0.654165i	$-0.226980\pi$
$107$	15.6475	1.51270	0.756352	+	0.654165i	$0.226980\pi$
$108$	1.27891	0.123063
$109$	−7.27822	−0.697127	−0.348563	−	0.937285i	$-0.613330\pi$
$109$	−7.27822	−0.697127	−0.348563	+	0.937285i	$0.613330\pi$
$110$	3.22476	0.307469
$111$	12.3231	1.16966
$112$	3.15095	0.297736
$113$	9.27667	0.872676	0.436338	−	0.899783i	$-0.356275\pi$
$113$	9.27667	0.872676	0.436338	+	0.899783i	$0.356275\pi$
$114$	5.84330	0.547275
$115$	−1.63400	−0.152371
$116$	2.29563	0.213144
$117$	−6.53981	−0.604605
$118$	−11.8178	−1.08792
$119$	−15.7733	−1.44593
$120$	2.02224	0.184604
$121$	5.53284	0.502985
$122$	−2.40674	−0.217896
$123$	20.3712	1.83681
$124$	3.84994	0.345735
$125$	7.43207	0.664745
$126$	−11.0333	−0.982921
$127$	13.1285	1.16497	0.582483	−	0.812843i	$-0.302081\pi$
$127$	13.1285	1.16497	0.582483	+	0.812843i	$0.302081\pi$
$128$	−1.00000	−0.0883883
$129$	8.61567	0.758567
$130$	−1.48124	−0.129914
$131$	22.2849	1.94704	0.973520	−	0.228602i	$-0.0734153\pi$
$131$	22.2849	1.94704	0.973520	+	0.228602i	$0.0734153\pi$
$132$	10.3677	0.902393
$133$	−7.22088	−0.626129
$134$	−7.94303	−0.686173
$135$	−1.01429	−0.0872964
$136$	5.00588	0.429250
$137$	−10.0348	−0.857331	−0.428665	−	0.903463i	$-0.641016\pi$
$137$	−10.0348	−0.857331	−0.428665	+	0.903463i	$0.641016\pi$
$138$	−5.25337	−0.447196
$139$	16.5627	1.40483	0.702414	−	0.711769i	$-0.252106\pi$
$139$	16.5627	1.40483	0.702414	+	0.711769i	$0.252106\pi$
$140$	−2.49899	−0.211203
$141$	−10.6293	−0.895146
$142$	5.71069	0.479230
$143$	−7.59410	−0.635050
$144$	3.50157	0.291797
$145$	−1.82064	−0.151196
$146$	10.3122	0.853446
$147$	7.46705	0.615872
$148$	4.83293	0.397264
$149$	−2.57531	−0.210977	−0.105489	−	0.994421i	$-0.533641\pi$
$149$	−2.57531	−0.210977	−0.105489	+	0.994421i	$0.533641\pi$
$150$	11.1453	0.910007
$151$	3.65526	0.297461	0.148730	−	0.988878i	$-0.452481\pi$
$151$	3.65526	0.297461	0.148730	+	0.988878i	$0.452481\pi$
$152$	2.29165	0.185878
$153$	−17.5284	−1.41709
$154$	−12.8119	−1.03242
$155$	−3.05336	−0.245251
$156$	−4.76224	−0.381284
$157$	12.7856	1.02040	0.510202	−	0.860055i	$-0.329571\pi$
$157$	12.7856	1.02040	0.510202	+	0.860055i	$0.329571\pi$
$158$	−8.43614	−0.671143
$159$	−2.20308	−0.174715
$160$	0.793092	0.0626994
$161$	6.49187	0.511631
$162$	7.24372	0.569121
$163$	−19.8392	−1.55392	−0.776961	−	0.629548i	$-0.783240\pi$
$163$	−19.8392	−1.55392	−0.776961	+	0.629548i	$0.783240\pi$
$164$	7.98927	0.623857
$165$	−8.22255	−0.640125
$166$	−11.1952	−0.868918
$167$	−6.36449	−0.492499	−0.246249	−	0.969206i	$-0.579198\pi$
$167$	−6.36449	−0.492499	−0.246249	+	0.969206i	$0.579198\pi$
$168$	−8.03434	−0.619863
$169$	−9.51177	−0.731675
$170$	−3.97012	−0.304494
$171$	−8.02438	−0.613640
$172$	3.37893	0.257641
$173$	2.52666	0.192099	0.0960493	−	0.995377i	$-0.469379\pi$
$173$	2.52666	0.192099	0.0960493	+	0.995377i	$0.469379\pi$
$174$	−5.85343	−0.443748
$175$	−13.7728	−1.04113
$176$	4.06606	0.306491
$177$	30.1333	2.26496
$178$	−10.6447	−0.797851
$179$	5.09766	0.381017	0.190508	−	0.981686i	$-0.438986\pi$
$179$	5.09766	0.381017	0.190508	+	0.981686i	$0.438986\pi$
$180$	−2.77707	−0.206990
$181$	15.5223	1.15376	0.576882	−	0.816828i	$-0.304269\pi$
$181$	15.5223	1.15376	0.576882	+	0.816828i	$0.304269\pi$
$182$	5.88496	0.436222
$183$	6.13675	0.453641
$184$	−2.06029	−0.151887
$185$	−3.83296	−0.281805
$186$	−9.81664	−0.719791
$187$	−20.3542	−1.48845
$188$	−4.16864	−0.304029
$189$	4.02977	0.293123
$190$	−1.81749	−0.131855
$191$	12.4003	0.897257	0.448628	−	0.893718i	$-0.351913\pi$
$191$	12.4003	0.897257	0.448628	+	0.893718i	$0.351913\pi$
$192$	2.54982	0.184017
$193$	0.905609	0.0651871	0.0325936	−	0.999469i	$-0.489623\pi$
$193$	0.905609	0.0651871	0.0325936	+	0.999469i	$0.489623\pi$
$194$	−2.85403	−0.204908
$195$	3.77690	0.270469
$196$	2.92847	0.209176
$197$	12.4247	0.885222	0.442611	−	0.896714i	$-0.354052\pi$
$197$	12.4247	0.885222	0.442611	+	0.896714i	$0.354052\pi$
$198$	−14.2376	−1.01182
$199$	−27.1519	−1.92475	−0.962375	−	0.271725i	$-0.912406\pi$
$199$	−27.1519	−1.92475	−0.962375	+	0.271725i	$0.912406\pi$
$200$	4.37100	0.309077
$201$	20.2533	1.42856
$202$	3.94531	0.277591
$203$	7.23340	0.507685
$204$	−12.7641	−0.893664
$205$	−6.33623	−0.442541
$206$	−10.4081	−0.725169
$207$	7.21425	0.501425
$208$	−1.86768	−0.129500
$209$	−9.31800	−0.644539
$210$	6.37197	0.439708
$211$	−15.3707	−1.05816	−0.529080	−	0.848572i	$-0.677463\pi$
$211$	−15.3707	−1.05816	−0.529080	+	0.848572i	$0.677463\pi$
$212$	−0.864013	−0.0593407
$213$	−14.5612	−0.997717
$214$	−15.6475	−1.06964
$215$	−2.67981	−0.182761
$216$	−1.27891	−0.0870187
$217$	12.1309	0.823502
$218$	7.27822	0.492943
$219$	−26.2943	−1.77680
$220$	−3.22476	−0.217413
$221$	9.34937	0.628907
$222$	−12.3231	−0.827072
$223$	−12.3192	−0.824952	−0.412476	−	0.910969i	$-0.635336\pi$
$223$	−12.3192	−0.824952	−0.412476	+	0.910969i	$0.635336\pi$
$224$	−3.15095	−0.210531
$225$	−15.3054	−1.02036
$226$	−9.27667	−0.617075
$227$	3.99048	0.264857	0.132429	−	0.991193i	$-0.457722\pi$
$227$	3.99048	0.264857	0.132429	+	0.991193i	$0.457722\pi$
$228$	−5.84330	−0.386982
$229$	4.46535	0.295079	0.147539	−	0.989056i	$-0.452865\pi$
$229$	4.46535	0.295079	0.147539	+	0.989056i	$0.452865\pi$
$230$	1.63400	0.107743
$231$	32.6681	2.14940
$232$	−2.29563	−0.150715
$233$	−19.1392	−1.25385	−0.626925	−	0.779079i	$-0.715687\pi$
$233$	−19.1392	−1.25385	−0.626925	+	0.779079i	$0.715687\pi$
$234$	6.53981	0.427521
$235$	3.30611	0.215667
$236$	11.8178	0.769275
$237$	21.5106	1.39726
$238$	15.7733	1.02243
$239$	−14.3312	−0.927009	−0.463505	−	0.886094i	$-0.653408\pi$
$239$	−14.3312	−0.927009	−0.463505	+	0.886094i	$0.653408\pi$
$240$	−2.02224	−0.130535
$241$	−6.12913	−0.394812	−0.197406	−	0.980322i	$-0.563252\pi$
$241$	−6.12913	−0.394812	−0.197406	+	0.980322i	$0.563252\pi$
$242$	−5.53284	−0.355664
$243$	−22.3069	−1.43099
$244$	2.40674	0.154076
$245$	−2.32254	−0.148382
$246$	−20.3712	−1.29882
$247$	4.28007	0.272335
$248$	−3.84994	−0.244471
$249$	28.5458	1.80902
$250$	−7.43207	−0.470045
$251$	−21.2238	−1.33963	−0.669816	−	0.742527i	$-0.733627\pi$
$251$	−21.2238	−1.33963	−0.669816	+	0.742527i	$0.733627\pi$
$252$	11.0333	0.695030
$253$	8.37726	0.526674
$254$	−13.1285	−0.823755
$255$	10.1231	0.633932
$256$	1.00000	0.0625000
$257$	24.5348	1.53044	0.765218	−	0.643771i	$-0.222631\pi$
$257$	24.5348	1.53044	0.765218	+	0.643771i	$0.222631\pi$
$258$	−8.61567	−0.536388
$259$	15.2283	0.946241
$260$	1.48124	0.0918627
$261$	8.03830	0.497558
$262$	−22.2849	−1.37677
$263$	−22.1136	−1.36358	−0.681790	−	0.731548i	$-0.738798\pi$
$263$	−22.1136	−1.36358	−0.681790	+	0.731548i	$0.738798\pi$
$264$	−10.3677	−0.638088
$265$	0.685242	0.0420941
$266$	7.22088	0.442740
$267$	27.1419	1.66106
$268$	7.94303	0.485198
$269$	−13.0356	−0.794793	−0.397397	−	0.917647i	$-0.630086\pi$
$269$	−13.0356	−0.794793	−0.397397	+	0.917647i	$0.630086\pi$
$270$	1.01429	0.0617279
$271$	−8.22476	−0.499618	−0.249809	−	0.968295i	$-0.580368\pi$
$271$	−8.22476	−0.499618	−0.249809	+	0.968295i	$0.580368\pi$
$272$	−5.00588	−0.303526
$273$	−15.0056	−0.908178
$274$	10.0348	0.606224
$275$	−17.7728	−1.07174
$276$	5.25337	0.316215
$277$	1.18928	0.0714567	0.0357283	−	0.999362i	$-0.488625\pi$
$277$	1.18928	0.0714567	0.0357283	+	0.999362i	$0.488625\pi$
$278$	−16.5627	−0.993363
$279$	13.4808	0.807076
$280$	2.49899	0.149343
$281$	−17.8202	−1.06306	−0.531531	−	0.847039i	$-0.678383\pi$
$281$	−17.8202	−1.06306	−0.531531	+	0.847039i	$0.678383\pi$
$282$	10.6293	0.632964
$283$	−14.1633	−0.841919	−0.420959	−	0.907079i	$-0.638307\pi$
$283$	−14.1633	−0.841919	−0.420959	+	0.907079i	$0.638307\pi$
$284$	−5.71069	−0.338867
$285$	4.63427	0.274511
$286$	7.59410	0.449048
$287$	25.1738	1.48596
$288$	−3.50157	−0.206332
$289$	8.05880	0.474047
$290$	1.82064	0.106912
$291$	7.27726	0.426601
$292$	−10.3122	−0.603478
$293$	10.4993	0.613378	0.306689	−	0.951810i	$-0.400779\pi$
$293$	10.4993	0.613378	0.306689	+	0.951810i	$0.400779\pi$
$294$	−7.46705	−0.435487
$295$	−9.37262	−0.545695
$296$	−4.83293	−0.280908
$297$	5.20012	0.301741
$298$	2.57531	0.149184
$299$	−3.84796	−0.222533
$300$	−11.1453	−0.643472
$301$	10.6468	0.613674
$302$	−3.65526	−0.210337
$303$	−10.0598	−0.577921
$304$	−2.29165	−0.131435
$305$	−1.90877	−0.109296
$306$	17.5284	1.00203
$307$	−5.98434	−0.341544	−0.170772	−	0.985311i	$-0.554626\pi$
$307$	−5.98434	−0.341544	−0.170772	+	0.985311i	$0.554626\pi$
$308$	12.8119	0.730028
$309$	26.5388	1.50974
$310$	3.05336	0.173419
$311$	0.830906	0.0471163	0.0235582	−	0.999722i	$-0.492501\pi$
$311$	0.830906	0.0471163	0.0235582	+	0.999722i	$0.492501\pi$
$312$	4.76224	0.269609
$313$	−18.6892	−1.05637	−0.528187	−	0.849128i	$-0.677128\pi$
$313$	−18.6892	−1.05637	−0.528187	+	0.849128i	$0.677128\pi$
$314$	−12.7856	−0.721534
$315$	−8.75039	−0.493029
$316$	8.43614	0.474570
$317$	29.5525	1.65983	0.829917	−	0.557888i	$-0.188388\pi$
$317$	29.5525	1.65983	0.829917	+	0.557888i	$0.188388\pi$
$318$	2.20308	0.123542
$319$	9.33416	0.522613
$320$	−0.793092	−0.0443352
$321$	39.8983	2.22691
$322$	−6.49187	−0.361778
$323$	11.4717	0.638304
$324$	−7.24372	−0.402429
$325$	8.16364	0.452837
$326$	19.8392	1.09879
$327$	−18.5581	−1.02627
$328$	−7.98927	−0.441134
$329$	−13.1352	−0.724165
$330$	8.22255	0.452636
$331$	−28.2621	−1.55342	−0.776712	−	0.629856i	$-0.783114\pi$
$331$	−28.2621	−1.55342	−0.776712	+	0.629856i	$0.783114\pi$
$332$	11.1952	0.614418
$333$	16.9228	0.927366
$334$	6.36449	0.348249
$335$	−6.29956	−0.344181
$336$	8.03434	0.438309
$337$	27.9567	1.52290	0.761449	−	0.648224i	$-0.224488\pi$
$337$	27.9567	1.52290	0.761449	+	0.648224i	$0.224488\pi$
$338$	9.51177	0.517372
$339$	23.6538	1.28470
$340$	3.97012	0.215310
$341$	15.6541	0.847716
$342$	8.02438	0.433909
$343$	−12.8292	−0.692711
$344$	−3.37893	−0.182180
$345$	−4.16640	−0.224312
$346$	−2.52666	−0.135834
$347$	−8.04210	−0.431723	−0.215861	−	0.976424i	$-0.569256\pi$
$347$	−8.04210	−0.431723	−0.215861	+	0.976424i	$0.569256\pi$
$348$	5.85343	0.313777
$349$	−3.73243	−0.199792	−0.0998962	−	0.994998i	$-0.531851\pi$
$349$	−3.73243	−0.199792	−0.0998962	+	0.994998i	$0.531851\pi$
$350$	13.7728	0.736187
$351$	−2.38859	−0.127494
$352$	−4.06606	−0.216722
$353$	31.7776	1.69135	0.845676	−	0.533697i	$-0.179198\pi$
$353$	31.7776	1.69135	0.845676	+	0.533697i	$0.179198\pi$
$354$	−30.1333	−1.60157
$355$	4.52910	0.240380
$356$	10.6447	0.564166
$357$	−40.2189	−2.12861
$358$	−5.09766	−0.269420
$359$	−11.1623	−0.589122	−0.294561	−	0.955633i	$-0.595173\pi$
$359$	−11.1623	−0.589122	−0.294561	+	0.955633i	$0.595173\pi$
$360$	2.77707	0.146364
$361$	−13.7483	−0.723596
$362$	−15.5223	−0.815834
$363$	14.1077	0.740464
$364$	−5.88496	−0.308456
$365$	8.17855	0.428085
$366$	−6.13675	−0.320773
$367$	−21.1271	−1.10283	−0.551414	−	0.834232i	$-0.685911\pi$
$367$	−21.1271	−1.10283	−0.551414	+	0.834232i	$0.685911\pi$
$368$	2.06029	0.107400
$369$	27.9750	1.45632
$370$	3.83296	0.199266
$371$	−2.72246	−0.141343
$372$	9.81664	0.508969
$373$	28.8309	1.49281	0.746403	−	0.665494i	$-0.231779\pi$
$373$	28.8309	1.49281	0.746403	+	0.665494i	$0.231779\pi$
$374$	20.3542	1.05249
$375$	18.9504	0.978596
$376$	4.16864	0.214981
$377$	−4.28750	−0.220817
$378$	−4.02977	−0.207269
$379$	18.2755	0.938750	0.469375	−	0.882999i	$-0.344479\pi$
$379$	18.2755	0.938750	0.469375	+	0.882999i	$0.344479\pi$
$380$	1.81749	0.0932354
$381$	33.4753	1.71499
$382$	−12.4003	−0.634456
$383$	17.0380	0.870601	0.435300	−	0.900285i	$-0.356642\pi$
$383$	17.0380	0.870601	0.435300	+	0.900285i	$0.356642\pi$
$384$	−2.54982	−0.130120
$385$	−10.1610	−0.517855
$386$	−0.905609	−0.0460943
$387$	11.8316	0.601433
$388$	2.85403	0.144892
$389$	−20.5537	−1.04211	−0.521057	−	0.853522i	$-0.674462\pi$
$389$	−20.5537	−1.04211	−0.521057	+	0.853522i	$0.674462\pi$
$390$	−3.77690	−0.191251
$391$	−10.3136	−0.521579
$392$	−2.92847	−0.147910
$393$	56.8224	2.86631
$394$	−12.4247	−0.625946
$395$	−6.69063	−0.336642
$396$	14.2376	0.715466
$397$	−17.6618	−0.886419	−0.443210	−	0.896418i	$-0.646160\pi$
$397$	−17.6618	−0.886419	−0.443210	+	0.896418i	$0.646160\pi$
$398$	27.1519	1.36100
$399$	−18.4119	−0.921749
$400$	−4.37100	−0.218550
$401$	−5.84532	−0.291901	−0.145951	−	0.989292i	$-0.546624\pi$
$401$	−5.84532	−0.291901	−0.145951	+	0.989292i	$0.546624\pi$
$402$	−20.2533	−1.01014
$403$	−7.19045	−0.358182
$404$	−3.94531	−0.196286
$405$	5.74494	0.285468
$406$	−7.23340	−0.358988
$407$	19.6510	0.974063
$408$	12.7641	0.631916
$409$	−18.7259	−0.925935	−0.462968	−	0.886375i	$-0.653215\pi$
$409$	−18.7259	−0.925935	−0.462968	+	0.886375i	$0.653215\pi$
$410$	6.33623	0.312924
$411$	−25.5869	−1.26211
$412$	10.4081	0.512772
$413$	37.2373	1.83233
$414$	−7.21425	−0.354561
$415$	−8.87885	−0.435845
$416$	1.86768	0.0915705
$417$	42.2318	2.06810
$418$	9.31800	0.455758
$419$	13.6512	0.666904	0.333452	−	0.942767i	$-0.391786\pi$
$419$	13.6512	0.666904	0.333452	+	0.942767i	$0.391786\pi$
$420$	−6.37197	−0.310920
$421$	−30.5351	−1.48819	−0.744096	−	0.668073i	$-0.767119\pi$
$421$	−30.5351	−1.48819	−0.744096	+	0.668073i	$0.767119\pi$
$422$	15.3707	0.748232
$423$	−14.5968	−0.709720
$424$	0.864013	0.0419602
$425$	21.8807	1.06137
$426$	14.5612	0.705493
$427$	7.58351	0.366992
$428$	15.6475	0.756352
$429$	−19.3636	−0.934881
$430$	2.67981	0.129232
$431$	7.63124	0.367584	0.183792	−	0.982965i	$-0.441163\pi$
$431$	7.63124	0.367584	0.183792	+	0.982965i	$0.441163\pi$
$432$	1.27891	0.0615315
$433$	15.3996	0.740057	0.370029	−	0.929020i	$-0.379348\pi$
$433$	15.3996	0.740057	0.370029	+	0.929020i	$0.379348\pi$
$434$	−12.1309	−0.582304
$435$	−4.64231	−0.222582
$436$	−7.27822	−0.348563
$437$	−4.72147	−0.225859
$438$	26.2943	1.25639
$439$	0.0682227	0.00325609	0.00162805	−	0.999999i	$-0.499482\pi$
$439$	0.0682227	0.00325609	0.00162805	+	0.999999i	$0.499482\pi$
$440$	3.22476	0.153734
$441$	10.2542	0.488296
$442$	−9.34937	−0.444704
$443$	22.4743	1.06779	0.533894	−	0.845552i	$-0.320728\pi$
$443$	22.4743	1.06779	0.533894	+	0.845552i	$0.320728\pi$
$444$	12.3231	0.584828
$445$	−8.44219	−0.400198
$446$	12.3192	0.583329
$447$	−6.56656	−0.310588
$448$	3.15095	0.148868
$449$	−34.2283	−1.61533	−0.807666	−	0.589640i	$-0.799270\pi$
$449$	−34.2283	−1.61533	−0.807666	+	0.589640i	$0.799270\pi$
$450$	15.3054	0.721502
$451$	32.4848	1.52965
$452$	9.27667	0.436338
$453$	9.32025	0.437903
$454$	−3.99048	−0.187282
$455$	4.66731	0.218807
$456$	5.84330	0.273637
$457$	25.7240	1.20332	0.601658	−	0.798754i	$-0.294507\pi$
$457$	25.7240	1.20332	0.601658	+	0.798754i	$0.294507\pi$
$458$	−4.46535	−0.208652
$459$	−6.40206	−0.298822
$460$	−1.63400	−0.0761857
$461$	−32.7913	−1.52724	−0.763620	−	0.645665i	$-0.776580\pi$
$461$	−32.7913	−1.52724	−0.763620	+	0.645665i	$0.776580\pi$
$462$	−32.6681	−1.51986
$463$	−2.63932	−0.122660	−0.0613298	−	0.998118i	$-0.519534\pi$
$463$	−2.63932	−0.122660	−0.0613298	+	0.998118i	$0.519534\pi$
$464$	2.29563	0.106572
$465$	−7.78550	−0.361044
$466$	19.1392	0.886606
$467$	−0.586704	−0.0271494	−0.0135747	−	0.999908i	$-0.504321\pi$
$467$	−0.586704	−0.0271494	−0.0135747	+	0.999908i	$0.504321\pi$
$468$	−6.53981	−0.302303
$469$	25.0281	1.15569
$470$	−3.30611	−0.152500
$471$	32.6010	1.50217
$472$	−11.8178	−0.543959
$473$	13.7389	0.631718
$474$	−21.5106	−0.988015
$475$	10.0168	0.459604
$476$	−15.7733	−0.722966
$477$	−3.02540	−0.138524
$478$	14.3312	0.655495
$479$	11.9546	0.546220	0.273110	−	0.961983i	$-0.411948\pi$
$479$	11.9546	0.546220	0.273110	+	0.961983i	$0.411948\pi$
$480$	2.02224	0.0923022
$481$	−9.02636	−0.411567
$482$	6.12913	0.279174
$483$	16.5531	0.753191
$484$	5.53284	0.251493
$485$	−2.26351	−0.102781
$486$	22.3069	1.01186
$487$	−13.2719	−0.601405	−0.300703	−	0.953718i	$-0.597221\pi$
$487$	−13.2719	−0.601405	−0.300703	+	0.953718i	$0.597221\pi$
$488$	−2.40674	−0.108948
$489$	−50.5862	−2.28759
$490$	2.32254	0.104922
$491$	−39.0869	−1.76397	−0.881984	−	0.471280i	$-0.843792\pi$
$491$	−39.0869	−1.76397	−0.881984	+	0.471280i	$0.843792\pi$
$492$	20.3712	0.918404
$493$	−11.4916	−0.517557
$494$	−4.28007	−0.192570
$495$	−11.2917	−0.507525
$496$	3.84994	0.172867
$497$	−17.9941	−0.807144
$498$	−28.5458	−1.27917
$499$	−0.785025	−0.0351426	−0.0175713	−	0.999846i	$-0.505593\pi$
$499$	−0.785025	−0.0351426	−0.0175713	+	0.999846i	$0.505593\pi$
$500$	7.43207	0.332372
$501$	−16.2283	−0.725026
$502$	21.2238	0.947263
$503$	12.9987	0.579585	0.289793	−	0.957089i	$-0.406414\pi$
$503$	12.9987	0.579585	0.289793	+	0.957089i	$0.406414\pi$
$504$	−11.0333	−0.491460
$505$	3.12899	0.139238
$506$	−8.37726	−0.372415
$507$	−24.2533	−1.07713
$508$	13.1285	0.582483
$509$	4.14358	0.183661	0.0918306	−	0.995775i	$-0.470728\pi$
$509$	4.14358	0.183661	0.0918306	+	0.995775i	$0.470728\pi$
$510$	−10.1231	−0.448258
$511$	−32.4933	−1.43742
$512$	−1.00000	−0.0441942
$513$	−2.93081	−0.129399
$514$	−24.5348	−1.08218
$515$	−8.25461	−0.363742
$516$	8.61567	0.379284
$517$	−16.9499	−0.745457
$518$	−15.2283	−0.669093
$519$	6.44253	0.282796
$520$	−1.48124	−0.0649568
$521$	0.348172	0.0152537	0.00762685	−	0.999971i	$-0.497572\pi$
$521$	0.348172	0.0152537	0.00762685	+	0.999971i	$0.497572\pi$
$522$	−8.03830	−0.351827
$523$	−30.1056	−1.31643	−0.658213	−	0.752832i	$-0.728687\pi$
$523$	−30.1056	−1.31643	−0.658213	+	0.752832i	$0.728687\pi$
$524$	22.2849	0.973520
$525$	−35.1181	−1.53268
$526$	22.1136	0.964197
$527$	−19.2723	−0.839515
$528$	10.3677	0.451197
$529$	−18.7552	−0.815444
$530$	−0.685242	−0.0297650
$531$	41.3809	1.79578
$532$	−7.22088	−0.313065
$533$	−14.9214	−0.646317
$534$	−27.1419	−1.17455
$535$	−12.4099	−0.536528
$536$	−7.94303	−0.343087
$537$	12.9981	0.560909
$538$	13.0356	0.562004
$539$	11.9073	0.512884
$540$	−1.01429	−0.0436482
$541$	−7.48018	−0.321598	−0.160799	−	0.986987i	$-0.551407\pi$
$541$	−7.48018	−0.321598	−0.160799	+	0.986987i	$0.551407\pi$
$542$	8.22476	0.353284
$543$	39.5790	1.69850
$544$	5.00588	0.214625
$545$	5.77230	0.247258
$546$	15.0056	0.642179
$547$	−4.64543	−0.198624	−0.0993122	−	0.995056i	$-0.531664\pi$
$547$	−4.64543	−0.198624	−0.0993122	+	0.995056i	$0.531664\pi$
$548$	−10.0348	−0.428665
$549$	8.42737	0.359671
$550$	17.7728	0.757833
$551$	−5.26078	−0.224117
$552$	−5.25337	−0.223598
$553$	26.5818	1.13037
$554$	−1.18928	−0.0505275
$555$	−9.77334	−0.414855
$556$	16.5627	0.702414
$557$	22.6233	0.958579	0.479289	−	0.877657i	$-0.340894\pi$
$557$	22.6233	0.958579	0.479289	+	0.877657i	$0.340894\pi$
$558$	−13.4808	−0.570689
$559$	−6.31077	−0.266917
$560$	−2.49899	−0.105602
$561$	−51.8995	−2.19120
$562$	17.8202	0.751699
$563$	−36.4023	−1.53417	−0.767086	−	0.641544i	$-0.778294\pi$
$563$	−36.4023	−1.53417	−0.767086	+	0.641544i	$0.778294\pi$
$564$	−10.6293	−0.447573
$565$	−7.35726	−0.309522
$566$	14.1633	0.595327
$567$	−22.8246	−0.958542
$568$	5.71069	0.239615
$569$	−23.2994	−0.976760	−0.488380	−	0.872631i	$-0.662412\pi$
$569$	−23.2994	−0.976760	−0.488380	+	0.872631i	$0.662412\pi$
$570$	−4.63427	−0.194108
$571$	21.9846	0.920025	0.460013	−	0.887912i	$-0.347845\pi$
$571$	21.9846	0.920025	0.460013	+	0.887912i	$0.347845\pi$
$572$	−7.59410	−0.317525
$573$	31.6186	1.32089
$574$	−25.1738	−1.05073
$575$	−9.00554	−0.375557
$576$	3.50157	0.145899
$577$	19.3938	0.807374	0.403687	−	0.914897i	$-0.367728\pi$
$577$	19.3938	0.807374	0.403687	+	0.914897i	$0.367728\pi$
$578$	−8.05880	−0.335202
$579$	2.30914	0.0959645
$580$	−1.82064	−0.0755981
$581$	35.2756	1.46348
$582$	−7.27726	−0.301652
$583$	−3.51313	−0.145499
$584$	10.3122	0.426723
$585$	5.18667	0.214442
$586$	−10.4993	−0.433724
$587$	17.7052	0.730773	0.365386	−	0.930856i	$-0.380937\pi$
$587$	17.7052	0.730773	0.365386	+	0.930856i	$0.380937\pi$
$588$	7.46705	0.307936
$589$	−8.82272	−0.363534
$590$	9.37262	0.385865
$591$	31.6807	1.30317
$592$	4.83293	0.198632
$593$	−16.1154	−0.661779	−0.330890	−	0.943669i	$-0.607349\pi$
$593$	−16.1154	−0.661779	−0.330890	+	0.943669i	$0.607349\pi$
$594$	−5.20012	−0.213363
$595$	12.5096	0.512845
$596$	−2.57531	−0.105489
$597$	−69.2325	−2.83350
$598$	3.84796	0.157355
$599$	25.7818	1.05341	0.526707	−	0.850047i	$-0.323426\pi$
$599$	25.7818	1.05341	0.526707	+	0.850047i	$0.323426\pi$
$600$	11.1453	0.455004
$601$	37.7516	1.53992	0.769960	−	0.638092i	$-0.220276\pi$
$601$	37.7516	1.53992	0.769960	+	0.638092i	$0.220276\pi$
$602$	−10.6468	−0.433933
$603$	27.8131	1.13264
$604$	3.65526	0.148730
$605$	−4.38805	−0.178400
$606$	10.0598	0.408652
$607$	0.512506	0.0208020	0.0104010	−	0.999946i	$-0.496689\pi$
$607$	0.512506	0.0208020	0.0104010	+	0.999946i	$0.496689\pi$
$608$	2.29165	0.0929388
$609$	18.4439	0.747383
$610$	1.90877	0.0772837
$611$	7.78568	0.314975
$612$	−17.5284	−0.708544
$613$	26.3613	1.06472	0.532362	−	0.846517i	$-0.321305\pi$
$613$	26.3613	1.06472	0.532362	+	0.846517i	$0.321305\pi$
$614$	5.98434	0.241508
$615$	−16.1562	−0.651482
$616$	−12.8119	−0.516208
$617$	11.0446	0.444640	0.222320	−	0.974974i	$-0.428637\pi$
$617$	11.0446	0.444640	0.222320	+	0.974974i	$0.428637\pi$
$618$	−26.5388	−1.06755
$619$	−16.0883	−0.646642	−0.323321	−	0.946289i	$-0.604799\pi$
$619$	−16.0883	−0.646642	−0.323321	+	0.946289i	$0.604799\pi$
$620$	−3.05336	−0.122626
$621$	2.63492	0.105736
$622$	−0.830906	−0.0333163
$623$	33.5407	1.34378
$624$	−4.76224	−0.190642
$625$	15.9607	0.638428
$626$	18.6892	0.746969
$627$	−23.7592	−0.948851
$628$	12.7856	0.510202
$629$	−24.1931	−0.964640
$630$	8.75039	0.348624
$631$	−13.7945	−0.549152	−0.274576	−	0.961565i	$-0.588537\pi$
$631$	−13.7945	−0.549152	−0.274576	+	0.961565i	$0.588537\pi$
$632$	−8.43614	−0.335571
$633$	−39.1924	−1.55776
$634$	−29.5525	−1.17368
$635$	−10.4121	−0.413192
$636$	−2.20308	−0.0873577
$637$	−5.46944	−0.216707
$638$	−9.33416	−0.369543
$639$	−19.9964	−0.791044
$640$	0.793092	0.0313497
$641$	−3.19475	−0.126185	−0.0630925	−	0.998008i	$-0.520096\pi$
$641$	−3.19475	−0.126185	−0.0630925	+	0.998008i	$0.520096\pi$
$642$	−39.8983	−1.57466
$643$	−29.6103	−1.16772	−0.583858	−	0.811856i	$-0.698458\pi$
$643$	−29.6103	−1.16772	−0.583858	+	0.811856i	$0.698458\pi$
$644$	6.49187	0.255815
$645$	−6.83302	−0.269050
$646$	−11.4717	−0.451349
$647$	−16.9733	−0.667289	−0.333644	−	0.942699i	$-0.608278\pi$
$647$	−16.9733	−0.667289	−0.333644	+	0.942699i	$0.608278\pi$
$648$	7.24372	0.284560
$649$	48.0520	1.88620
$650$	−8.16364	−0.320204
$651$	30.9317	1.21231
$652$	−19.8392	−0.776961
$653$	47.0584	1.84154	0.920768	−	0.390111i	$-0.127563\pi$
$653$	47.0584	1.84154	0.920768	+	0.390111i	$0.127563\pi$
$654$	18.5581	0.725680
$655$	−17.6740	−0.690579
$656$	7.98927	0.311929
$657$	−36.1090	−1.40875
$658$	13.1352	0.512062
$659$	21.7003	0.845322	0.422661	−	0.906288i	$-0.361096\pi$
$659$	21.7003	0.845322	0.422661	+	0.906288i	$0.361096\pi$
$660$	−8.22255	−0.320062
$661$	7.25797	0.282302	0.141151	−	0.989988i	$-0.454920\pi$
$661$	7.25797	0.282302	0.141151	+	0.989988i	$0.454920\pi$
$662$	28.2621	1.09844
$663$	23.8392	0.925838
$664$	−11.1952	−0.434459
$665$	5.72682	0.222077
$666$	−16.9228	−0.655747
$667$	4.72966	0.183133
$668$	−6.36449	−0.246249
$669$	−31.4116	−1.21444
$670$	6.29956	0.243373
$671$	9.78595	0.377782
$672$	−8.03434	−0.309931
$673$	25.7669	0.993243	0.496621	−	0.867967i	$-0.334574\pi$
$673$	25.7669	0.993243	0.496621	+	0.867967i	$0.334574\pi$
$674$	−27.9567	−1.07685
$675$	−5.59012	−0.215164
$676$	−9.51177	−0.365837
$677$	33.6159	1.29196	0.645982	−	0.763353i	$-0.276448\pi$
$677$	33.6159	1.29196	0.645982	+	0.763353i	$0.276448\pi$
$678$	−23.6538	−0.908419
$679$	8.99290	0.345116
$680$	−3.97012	−0.152247
$681$	10.1750	0.389907
$682$	−15.6541	−0.599425
$683$	−19.9765	−0.764381	−0.382191	−	0.924084i	$-0.624830\pi$
$683$	−19.9765	−0.764381	−0.382191	+	0.924084i	$0.624830\pi$
$684$	−8.02438	−0.306820
$685$	7.95852	0.304079
$686$	12.8292	0.489821
$687$	11.3858	0.434397
$688$	3.37893	0.128821
$689$	1.61370	0.0614771
$690$	4.16640	0.158612
$691$	−30.9497	−1.17738	−0.588690	−	0.808359i	$-0.700356\pi$
$691$	−30.9497	−1.17738	−0.588690	+	0.808359i	$0.700356\pi$
$692$	2.52666	0.0960493
$693$	44.8619	1.70416
$694$	8.04210	0.305274
$695$	−13.1357	−0.498267
$696$	−5.85343	−0.221874
$697$	−39.9933	−1.51485
$698$	3.73243	0.141275
$699$	−48.8015	−1.84584
$700$	−13.7728	−0.520563
$701$	11.0205	0.416238	0.208119	−	0.978103i	$-0.433266\pi$
$701$	11.0205	0.416238	0.208119	+	0.978103i	$0.433266\pi$
$702$	2.38859	0.0901516
$703$	−11.0754	−0.417717
$704$	4.06606	0.153245
$705$	8.42999	0.317492
$706$	−31.7776	−1.19597
$707$	−12.4315	−0.467533
$708$	30.1333	1.13248
$709$	−16.0603	−0.603159	−0.301579	−	0.953441i	$-0.597514\pi$
$709$	−16.0603	−0.603159	−0.301579	+	0.953441i	$0.597514\pi$
$710$	−4.52910	−0.169974
$711$	29.5397	1.10783
$712$	−10.6447	−0.398925
$713$	7.93199	0.297055
$714$	40.2189	1.50515
$715$	6.02282	0.225241
$716$	5.09766	0.190508
$717$	−36.5420	−1.36469
$718$	11.1623	0.416572
$719$	−0.534652	−0.0199392	−0.00996958	−	0.999950i	$-0.503173\pi$
$719$	−0.534652	−0.0199392	−0.00996958	+	0.999950i	$0.503173\pi$
$720$	−2.77707	−0.103495
$721$	32.7955	1.22137
$722$	13.7483	0.511660
$723$	−15.6282	−0.581218
$724$	15.5223	0.576882
$725$	−10.0342	−0.372661
$726$	−14.1077	−0.523587
$727$	−44.2730	−1.64199	−0.820997	−	0.570932i	$-0.806582\pi$
$727$	−44.2730	−1.64199	−0.820997	+	0.570932i	$0.806582\pi$
$728$	5.88496	0.218111
$729$	−35.1473	−1.30175
$730$	−8.17855	−0.302702
$731$	−16.9145	−0.625607
$732$	6.13675	0.226821
$733$	−21.3214	−0.787525	−0.393763	−	0.919212i	$-0.628827\pi$
$733$	−21.3214	−0.787525	−0.393763	+	0.919212i	$0.628827\pi$
$734$	21.1271	0.779817
$735$	−5.92206	−0.218439
$736$	−2.06029	−0.0759433
$737$	32.2968	1.18967
$738$	−27.9750	−1.02977
$739$	−11.4734	−0.422055	−0.211027	−	0.977480i	$-0.567681\pi$
$739$	−11.4734	−0.422055	−0.211027	+	0.977480i	$0.567681\pi$
$740$	−3.83296	−0.140902
$741$	10.9134	0.400914
$742$	2.72246	0.0999447
$743$	0.0693300	0.00254347	0.00127174	−	0.999999i	$-0.499595\pi$
$743$	0.0693300	0.00254347	0.00127174	+	0.999999i	$0.499595\pi$
$744$	−9.81664	−0.359895
$745$	2.04246	0.0748298
$746$	−28.8309	−1.05557
$747$	39.2009	1.43428
$748$	−20.3542	−0.744223
$749$	49.3045	1.80155
$750$	−18.9504	−0.691972
$751$	−4.93213	−0.179976	−0.0899880	−	0.995943i	$-0.528683\pi$
$751$	−4.93213	−0.179976	−0.0899880	+	0.995943i	$0.528683\pi$
$752$	−4.16864	−0.152015
$753$	−54.1167	−1.97212
$754$	4.28750	0.156141
$755$	−2.89896	−0.105504
$756$	4.02977	0.146561
$757$	4.57119	0.166143	0.0830713	−	0.996544i	$-0.473527\pi$
$757$	4.57119	0.166143	0.0830713	+	0.996544i	$0.473527\pi$
$758$	−18.2755	−0.663796
$759$	21.3605	0.775337
$760$	−1.81749	−0.0659274
$761$	15.9198	0.577092	0.288546	−	0.957466i	$-0.406828\pi$
$761$	15.9198	0.577092	0.288546	+	0.957466i	$0.406828\pi$
$762$	−33.4753	−1.21268
$763$	−22.9333	−0.830240
$764$	12.4003	0.448628
$765$	13.9017	0.502615
$766$	−17.0380	−0.615608
$767$	−22.0719	−0.796970
$768$	2.54982	0.0920086
$769$	−33.7117	−1.21567	−0.607837	−	0.794062i	$-0.707963\pi$
$769$	−33.7117	−1.21567	−0.607837	+	0.794062i	$0.707963\pi$
$770$	10.1610	0.366179
$771$	62.5591	2.25301
$772$	0.905609	0.0325936
$773$	8.34690	0.300217	0.150109	−	0.988670i	$-0.452038\pi$
$773$	8.34690	0.300217	0.150109	+	0.988670i	$0.452038\pi$
$774$	−11.8316	−0.425277
$775$	−16.8281	−0.604483
$776$	−2.85403	−0.102454
$777$	38.8294	1.39300
$778$	20.5537	0.736886
$779$	−18.3086	−0.655975
$780$	3.77690	0.135235
$781$	−23.2200	−0.830876
$782$	10.3136	0.368812
$783$	2.93590	0.104920
$784$	2.92847	0.104588
$785$	−10.1402	−0.361918
$786$	−56.8224	−2.02679
$787$	20.8114	0.741847	0.370924	−	0.928663i	$-0.379041\pi$
$787$	20.8114	0.741847	0.370924	+	0.928663i	$0.379041\pi$
$788$	12.4247	0.442611
$789$	−56.3855	−2.00738
$790$	6.69063	0.238042
$791$	29.2303	1.03931
$792$	−14.2376	−0.505911
$793$	−4.49502	−0.159623
$794$	17.6618	0.626793
$795$	1.74724	0.0619683
$796$	−27.1519	−0.962375
$797$	15.8001	0.559670	0.279835	−	0.960048i	$-0.409720\pi$
$797$	15.8001	0.559670	0.279835	+	0.960048i	$0.409720\pi$
$798$	18.4119	0.651775
$799$	20.8677	0.738246
$800$	4.37100	0.154538
$801$	37.2730	1.31698
$802$	5.84532	0.206405
$803$	−41.9301	−1.47968
$804$	20.2533	0.714278
$805$	−5.14865	−0.181466
$806$	7.19045	0.253273
$807$	−33.2383	−1.17004
$808$	3.94531	0.138795
$809$	36.0919	1.26892	0.634461	−	0.772955i	$-0.281222\pi$
$809$	36.0919	1.26892	0.634461	+	0.772955i	$0.281222\pi$
$810$	−5.74494	−0.201857
$811$	−3.12850	−0.109856	−0.0549282	−	0.998490i	$-0.517493\pi$
$811$	−3.12850	−0.109856	−0.0549282	+	0.998490i	$0.517493\pi$
$812$	7.23340	0.253843
$813$	−20.9716	−0.735507
$814$	−19.6510	−0.688766
$815$	15.7343	0.551148
$816$	−12.7641	−0.446832
$817$	−7.74335	−0.270905
$818$	18.7259	0.654735
$819$	−20.6066	−0.720052
$820$	−6.33623	−0.221271
$821$	10.8682	0.379301	0.189651	−	0.981852i	$-0.439264\pi$
$821$	10.8682	0.379301	0.189651	+	0.981852i	$0.439264\pi$
$822$	25.5869	0.892446
$823$	−3.96040	−0.138051	−0.0690254	−	0.997615i	$-0.521989\pi$
$823$	−3.96040	−0.138051	−0.0690254	+	0.997615i	$0.521989\pi$
$824$	−10.4081	−0.362585
$825$	−45.3173	−1.57775
$826$	−37.2373	−1.29565
$827$	25.9632	0.902828	0.451414	−	0.892315i	$-0.350920\pi$
$827$	25.9632	0.902828	0.451414	+	0.892315i	$0.350920\pi$
$828$	7.21425	0.250713
$829$	−35.8260	−1.24429	−0.622144	−	0.782903i	$-0.713738\pi$
$829$	−35.8260	−1.24429	−0.622144	+	0.782903i	$0.713738\pi$
$830$	8.87885	0.308189
$831$	3.03244	0.105194
$832$	−1.86768	−0.0647501
$833$	−14.6595	−0.507923
$834$	−42.2318	−1.46237
$835$	5.04763	0.174680
$836$	−9.31800	−0.322270
$837$	4.92372	0.170189
$838$	−13.6512	−0.471572
$839$	19.4313	0.670843	0.335422	−	0.942068i	$-0.391121\pi$
$839$	19.4313	0.670843	0.335422	+	0.942068i	$0.391121\pi$
$840$	6.37197	0.219854
$841$	−23.7301	−0.818279
$842$	30.5351	1.05231
$843$	−45.4382	−1.56497
$844$	−15.3707	−0.529080
$845$	7.54371	0.259512
$846$	14.5968	0.501848
$847$	17.4337	0.599028
$848$	−0.864013	−0.0296703
$849$	−36.1137	−1.23942
$850$	−21.8807	−0.750502
$851$	9.95724	0.341330
$852$	−14.5612	−0.498859
$853$	−3.03043	−0.103760	−0.0518800	−	0.998653i	$-0.516521\pi$
$853$	−3.03043	−0.103760	−0.0518800	+	0.998653i	$0.516521\pi$
$854$	−7.58351	−0.259502
$855$	6.36407	0.217647
$856$	−15.6475	−0.534822
$857$	1.32742	0.0453439	0.0226719	−	0.999743i	$-0.492783\pi$
$857$	1.32742	0.0453439	0.0226719	+	0.999743i	$0.492783\pi$
$858$	19.3636	0.661061
$859$	−13.3815	−0.456570	−0.228285	−	0.973594i	$-0.573312\pi$
$859$	−13.3815	−0.456570	−0.228285	+	0.973594i	$0.573312\pi$
$860$	−2.67981	−0.0913806
$861$	64.1885	2.18754
$862$	−7.63124	−0.259921
$863$	−45.9682	−1.56478	−0.782388	−	0.622792i	$-0.785998\pi$
$863$	−45.9682	−1.56478	−0.782388	+	0.622792i	$0.785998\pi$
$864$	−1.27891	−0.0435093
$865$	−2.00388	−0.0681338
$866$	−15.3996	−0.523299
$867$	20.5485	0.697863
$868$	12.1309	0.411751
$869$	34.3018	1.16361
$870$	4.64231	0.157389
$871$	−14.8350	−0.502666
$872$	7.27822	0.246472
$873$	9.99359	0.338232
$874$	4.72147	0.159706
$875$	23.4181	0.791675
$876$	−26.2943	−0.888402
$877$	−19.8402	−0.669955	−0.334978	−	0.942226i	$-0.608729\pi$
$877$	−19.8402	−0.669955	−0.334978	+	0.942226i	$0.608729\pi$
$878$	−0.0682227	−0.00230241
$879$	26.7714	0.902977
$880$	−3.22476	−0.108707
$881$	−11.1724	−0.376407	−0.188203	−	0.982130i	$-0.560266\pi$
$881$	−11.1724	−0.376407	−0.188203	+	0.982130i	$0.560266\pi$
$882$	−10.2542	−0.345278
$883$	−10.5446	−0.354855	−0.177428	−	0.984134i	$-0.556778\pi$
$883$	−10.5446	−0.354855	−0.177428	+	0.984134i	$0.556778\pi$
$884$	9.34937	0.314453
$885$	−23.8985	−0.803338
$886$	−22.4743	−0.755040
$887$	0.674443	0.0226456	0.0113228	−	0.999936i	$-0.496396\pi$
$887$	0.674443	0.0226456	0.0113228	+	0.999936i	$0.496396\pi$
$888$	−12.3231	−0.413536
$889$	41.3672	1.38741
$890$	8.44219	0.282983
$891$	−29.4534	−0.986726
$892$	−12.3192	−0.412476
$893$	9.55308	0.319681
$894$	6.56656	0.219619
$895$	−4.04291	−0.135140
$896$	−3.15095	−0.105266
$897$	−9.81160	−0.327600
$898$	34.2283	1.14221
$899$	8.83802	0.294765
$900$	−15.3054	−0.510179
$901$	4.32514	0.144091
$902$	−32.4848	−1.08163
$903$	27.1475	0.903412
$904$	−9.27667	−0.308538
$905$	−12.3106	−0.409219
$906$	−9.32025	−0.309645
$907$	3.34433	0.111047	0.0555233	−	0.998457i	$-0.482317\pi$
$907$	3.34433	0.111047	0.0555233	+	0.998457i	$0.482317\pi$
$908$	3.99048	0.132429
$909$	−13.8148	−0.458207
$910$	−4.66731	−0.154720
$911$	13.4016	0.444013	0.222007	−	0.975045i	$-0.428739\pi$
$911$	13.4016	0.444013	0.222007	+	0.975045i	$0.428739\pi$
$912$	−5.84330	−0.193491
$913$	45.5205	1.50651
$914$	−25.7240	−0.850873
$915$	−4.86701	−0.160898
$916$	4.46535	0.147539
$917$	70.2185	2.31882
$918$	6.40206	0.211299
$919$	52.6575	1.73701	0.868505	−	0.495680i	$-0.165081\pi$
$919$	52.6575	1.73701	0.868505	+	0.495680i	$0.165081\pi$
$920$	1.63400	0.0538714
$921$	−15.2590	−0.502800
$922$	32.7913	1.07992
$923$	10.6657	0.351067
$924$	32.6681	1.07470
$925$	−21.1248	−0.694578
$926$	2.63932	0.0867335
$927$	36.4448	1.19700
$928$	−2.29563	−0.0753577
$929$	−28.3539	−0.930261	−0.465130	−	0.885242i	$-0.653993\pi$
$929$	−28.3539	−0.930261	−0.465130	+	0.885242i	$0.653993\pi$
$930$	7.78550	0.255297
$931$	−6.71103	−0.219945
$932$	−19.1392	−0.626925
$933$	2.11866	0.0693617
$934$	0.586704	0.0191976
$935$	16.1427	0.527924
$936$	6.53981	0.213760
$937$	−26.9537	−0.880540	−0.440270	−	0.897865i	$-0.645117\pi$
$937$	−26.9537	−0.880540	−0.440270	+	0.897865i	$0.645117\pi$
$938$	−25.0281	−0.817195
$939$	−47.6540	−1.55513
$940$	3.30611	0.107834
$941$	25.3302	0.825742	0.412871	−	0.910789i	$-0.364526\pi$
$941$	25.3302	0.825742	0.412871	+	0.910789i	$0.364526\pi$
$942$	−32.6010	−1.06220
$943$	16.4602	0.536018
$944$	11.8178	0.384637
$945$	−3.19598	−0.103965
$946$	−13.7389	−0.446692
$947$	−26.9170	−0.874685	−0.437342	−	0.899295i	$-0.644080\pi$
$947$	−26.9170	−0.874685	−0.437342	+	0.899295i	$0.644080\pi$
$948$	21.5106	0.698632
$949$	19.2599	0.625204
$950$	−10.0168	−0.324989
$951$	75.3534	2.44350
$952$	15.7733	0.511214
$953$	−46.7016	−1.51281	−0.756407	−	0.654101i	$-0.773047\pi$
$953$	−46.7016	−1.51281	−0.756407	+	0.654101i	$0.773047\pi$
$954$	3.02540	0.0979510
$955$	−9.83461	−0.318240
$956$	−14.3312	−0.463505
$957$	23.8004	0.769358
$958$	−11.9546	−0.386236
$959$	−31.6191	−1.02103
$960$	−2.02224	−0.0652675
$961$	−16.1780	−0.521870
$962$	9.02636	0.291022
$963$	54.7909	1.76561
$964$	−6.12913	−0.197406
$965$	−0.718231	−0.0231207
$966$	−16.5531	−0.532586
$967$	44.3301	1.42556	0.712779	−	0.701388i	$-0.247436\pi$
$967$	44.3301	1.42556	0.712779	+	0.701388i	$0.247436\pi$
$968$	−5.53284	−0.177832
$969$	29.2508	0.939672
$970$	2.26351	0.0726769
$971$	39.8581	1.27911	0.639554	−	0.768746i	$-0.279119\pi$
$971$	39.8581	1.27911	0.639554	+	0.768746i	$0.279119\pi$
$972$	−22.3069	−0.715494
$973$	52.1881	1.67307
$974$	13.2719	0.425258
$975$	20.8158	0.666639
$976$	2.40674	0.0770379
$977$	−24.4253	−0.781435	−0.390717	−	0.920511i	$-0.627773\pi$
$977$	−24.4253	−0.781435	−0.390717	+	0.920511i	$0.627773\pi$
$978$	50.5862	1.61757
$979$	43.2818	1.38329
$980$	−2.32254	−0.0741909
$981$	−25.4852	−0.813679
$982$	39.0869	1.24731
$983$	4.92539	0.157096	0.0785478	−	0.996910i	$-0.474972\pi$
$983$	4.92539	0.157096	0.0785478	+	0.996910i	$0.474972\pi$
$984$	−20.3712	−0.649409
$985$	−9.85392	−0.313972
$986$	11.4916	0.365968
$987$	−33.4923	−1.06607
$988$	4.28007	0.136167
$989$	6.96159	0.221366
$990$	11.2917	0.358874
$991$	−32.9541	−1.04682	−0.523411	−	0.852081i	$-0.675341\pi$
$991$	−32.9541	−1.04682	−0.523411	+	0.852081i	$0.675341\pi$
$992$	−3.84994	−0.122236
$993$	−72.0631	−2.28685
$994$	17.9941	0.570737
$995$	21.5340	0.682673
$996$	28.5458	0.904508
$997$	−4.23171	−0.134020	−0.0670099	−	0.997752i	$-0.521346\pi$
$997$	−4.23171	−0.134020	−0.0670099	+	0.997752i	$0.521346\pi$
$998$	0.785025	0.0248495
$999$	6.18087	0.195554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.67	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.67	✓	77	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.54982 q^{3} +1.00000 q^{4} -0.793092 q^{5} -2.54982 q^{6} +3.15095 q^{7} -1.00000 q^{8} +3.50157 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.54982 q^{3} +1.00000 q^{4} -0.793092 q^{5} -2.54982 q^{6} +3.15095 q^{7} -1.00000 q^{8} +3.50157 q^{9} +0.793092 q^{10} +4.06606 q^{11} +2.54982 q^{12} -1.86768 q^{13} -3.15095 q^{14} -2.02224 q^{15} +1.00000 q^{16} -5.00588 q^{17} -3.50157 q^{18} -2.29165 q^{19} -0.793092 q^{20} +8.03434 q^{21} -4.06606 q^{22} +2.06029 q^{23} -2.54982 q^{24} -4.37100 q^{25} +1.86768 q^{26} +1.27891 q^{27} +3.15095 q^{28} +2.29563 q^{29} +2.02224 q^{30} +3.84994 q^{31} -1.00000 q^{32} +10.3677 q^{33} +5.00588 q^{34} -2.49899 q^{35} +3.50157 q^{36} +4.83293 q^{37} +2.29165 q^{38} -4.76224 q^{39} +0.793092 q^{40} +7.98927 q^{41} -8.03434 q^{42} +3.37893 q^{43} +4.06606 q^{44} -2.77707 q^{45} -2.06029 q^{46} -4.16864 q^{47} +2.54982 q^{48} +2.92847 q^{49} +4.37100 q^{50} -12.7641 q^{51} -1.86768 q^{52} -0.864013 q^{53} -1.27891 q^{54} -3.22476 q^{55} -3.15095 q^{56} -5.84330 q^{57} -2.29563 q^{58} +11.8178 q^{59} -2.02224 q^{60} +2.40674 q^{61} -3.84994 q^{62} +11.0333 q^{63} +1.00000 q^{64} +1.48124 q^{65} -10.3677 q^{66} +7.94303 q^{67} -5.00588 q^{68} +5.25337 q^{69} +2.49899 q^{70} -5.71069 q^{71} -3.50157 q^{72} -10.3122 q^{73} -4.83293 q^{74} -11.1453 q^{75} -2.29165 q^{76} +12.8119 q^{77} +4.76224 q^{78} +8.43614 q^{79} -0.793092 q^{80} -7.24372 q^{81} -7.98927 q^{82} +11.1952 q^{83} +8.03434 q^{84} +3.97012 q^{85} -3.37893 q^{86} +5.85343 q^{87} -4.06606 q^{88} +10.6447 q^{89} +2.77707 q^{90} -5.88496 q^{91} +2.06029 q^{92} +9.81664 q^{93} +4.16864 q^{94} +1.81749 q^{95} -2.54982 q^{96} +2.85403 q^{97} -2.92847 q^{98} +14.2376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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